A Continuous Latent Spatial Model for Crack Initiation in Bone Cement

Hip replacements provide a means of achieving a higher quality of life for individuals who have, through aging or injury, accumulated damage to their natural joints. This is a very common operation, with over a million people a year benefiting from the procedure. The replacements themselves fail mainly as a result of the mechanical loosening of the components of the artificial joint due to damage accumulation occurring. This damage accumulation consists of the initiation and growth of cracks in the bone cement which is used to fixate the replacement in the human body. The data come from laboratory experiments designed to assess the effectiveness of the bone cement in resisting damage. In this paper we examine the properties of the bone cement, with the aim being to estimate the impact that both observable and unobservable spatially varying factors have on causing crack initiation. To do this, an explicit model for the damage process is constructed taking into account the tension and compression at different locations in the specimens. A Gamma random field is used to model any latent spatial factors that may be influential in crack initiation. Bayesian inference is carried out for the parameters of this field and related covariates using Markov chain Monte Carlo techniques.